Problem 3-42/3-43/3-44/ Engineering Mechanics Materials

Engineering Mechanics problem with solution.
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3–42. The pipe with two rigid caps attached to its ends is subjected to an axial force P . If the pipe is made from a material having a modulus of elasticity E and Poisson’s ratio n, determine the change in volume of the material.

3–43. The 8-mm-diameter bolt is made of an aluminum alloy. It fits through a magnesium sleeve that has an inner diameter of 12 mm and an outer diameter of 20 mm. If the original lengths of the bolt and sleeve are 80 mm and
50 mm, respectively, determine the strains in the sleeve and the bolt if the nut on the bolt is tightened so that the tension in the bolt is 8 kN. Assume the material at A is rigid. Eal = 70 GPa, Emg = 45 GPa.

3–44. An acetal polymer block is fixed to the rigid plates at its top and bottom surfaces. If the top plate displaces 2 mm horizontally when it is subjected to a horizontal force
P = 2 kN, determine the shear modulus of the polymer. The width of the block is 100 mm. Assume that the polymer is linearly elastic and use small angle analysis.